On Sampling Edges Almost Uniformly

Eden, Talya; Rosenbaum, Will

doi:10.4230/OASIcs.SOSA.2018.7

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Sublinear Algorithms
Graph Algorithms
Sampling Edges
Query Complexity

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Abstract

We consider the problem of sampling an edge almost uniformly from an unknown graph, G = (V, E). Access to the graph is provided via queries of the following types: (1) uniform vertex queries, (2) degree queries, and (3) neighbor queries. We describe a new simple algorithm that returns a random edge e in E using \tilde{O}(n/sqrt{eps m}) queries in expectation, such that each edge e is sampled with probability (1 +/- eps)/m. Here, n = |V| is the number of vertices, and m = |E| is the number of edges. Our algorithm is optimal in the sense that any algorithm that samples an edge from an almost-uniform distribution must perform Omega(n/sqrt{m}) queries.

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Talya Eden and Will Rosenbaum. On Sampling Edges Almost Uniformly. In 1st Symposium on Simplicity in Algorithms (SOSA 2018). Open Access Series in Informatics (OASIcs), Volume 61, pp. 7:1-7:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/OASIcs.SOSA.2018.7

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Talya Eden

Will Rosenbaum

References

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Talya Eden, Dana Ron, and C. Seshadhri. Sublinear time estimation of degree distribution moments: The degeneracy connection. In Ioannis Chatzigiannakis, Piotr Indyk, Fabian Kuhn, and Anca Muscholl, editors, 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017, July 10-14, 2017, Warsaw, Poland, volume 80 of LIPIcs, pages 7:1-7:13. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2017. URL: http://dx.doi.org/10.4230/LIPIcs.ICALP.2017.7.
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On Sampling Edges Almost Uniformly

Authors Talya Eden, Will Rosenbaum

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